Atlas › Modular forms › Weight 2 › Level 933 › 933.2.a

Newspace 933.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(933))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
933.2.a.a	1	$\mathbb{Q}$	$q - q^{3} - 2q^{4} - q^{7} + O(q^{8})$	+ +	$-1$	933a1 rank 1
933.2.a.b	1	$\mathbb{Q}$	$q + q^{3} - 2q^{4} - 2q^{5} + 3q^{7} + O(q^{8})$	− −	$-1$	933b1 rank 1
933.2.a.c	10	degree 10	$10q - 7q^{2} + 10q^{3} + 9q^{4} - 6q^{5} - 7q^{6} - 14q^{7} + O(q^{8})$	− −	$-1$
933.2.a.d	10	degree 10	$10q - q^{2} - 10q^{3} + 9q^{4} - 2q^{5} + q^{6} - 10q^{7} + O(q^{8})$	+ +	$-1$
933.2.a.e	14	degree 14	$14q + 4q^{2} + 14q^{3} + 12q^{4} + 6q^{5} + 4q^{6} + 5q^{7} + O(q^{8})$	− +	$+1$
933.2.a.f	15	degree 15	$15q + q^{2} - 15q^{3} + 19q^{4} + 2q^{5} - q^{6} + 13q^{7} + O(q^{8})$	+ −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{5}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
933.2.a.a	$x$
933.2.a.b	$x + 2$
933.2.a.c	$x^{10} + 13x^{9} + 44x^{8} - 61x^{7} - 575x^{6} - 684x^{5} + 1160x^{4} + 2968x^{3} + 1538x^{2} - 402x - 293$
933.2.a.d	$x^{10} + 3x^{9} - 24x^{8} - 75x^{7} + 121x^{6} + 500x^{5} + 234x^{4} - 292x^{3} - 114x^{2} + 74x - 7$
933.2.a.e	$x^{14} - 10x^{13} - 6x^{12} + 347x^{11} - 795x^{10} - 3114x^{9} + 13026x^{8} + 929x^{7} - 57376x^{6} + 49124x^{5} + 78711x^{4} - 104521x^{3} - 22903x^{2} + 57561x - 11930$
933.2.a.f	$x^{15} - 3x^{14} - 78x^{13} + 195x^{12} + 2288x^{11} - 4721x^{10} - 31376x^{9} + 51573x^{8} + 201605x^{7} - 241486x^{6} - 535277x^{5} + 346438x^{4} + 637666x^{3} - 53960x^{2} - 236737x - 58792$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(933))$	51
Old forms	52
Cusp forms $S_{2}(\Gamma_0(933))$	103
Eisenstein series $E_{2}(\Gamma_0(933))$	3
Modular forms $M_{2}(\Gamma_0(933))$	106

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(933)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(311))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.275 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks

dim M^+ at levels [1, 3, 311, 933]: [0, 1, 27, 106] (certified at ell = 2147479121)
T = [(2, 1), (5, 1)]; h of degree 51 = 1 x 51 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(933, 2)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 933:2 1000

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